Dfyjkt

I am currently in Saint Petersburg on a tourist visa (I'm French). I arrived on Tuesday and I'm leaving on Wednesday morning, so I will be a total of 7 working days in Russia, including the arrival and departure days.
I assumed I wouldn't need to register my visa, so I didn't, and neither the hostel where I'm staying nor my sponsor told me anything about it either.

Now I just noticed that because of the world cup the rules have changed, and I was actually supposed to register it within 24 hours, so it's obviously too late now.

What should I do? Should I go try to register it anyway before leaving (and pay whatever fine there is) or should I just forget about it and hope they won't care? Is there a risk they will prevent me from leaving Russia?

In case that matters, I will be leaving by train to Finland (and on the last day of my visa).

As OP has not returned to TSE, here are the requirements and the implications for failure to register:

Russia Visa Registration and Migration Cards

According to Russian law, each foreigner entering the territory of the Russian Federation should register his or her visa within 72 hours upon arrival, except for weekends and official state holidays. Failure to register a visa may lead to detention by the Russian police, fines and other inconveniences. To register the visa, one needs a migration card [see sample].

The migration card should be filled out by every foreigner entering Russia. It consists of two sections [see sample]. The top part of the card is collected by the passport/visa control officials, while the bottom part is collected when the person leaves the country to return home. Migration cards serve as a statistical tool and a record of entry, exit, and registration. The card is also necessary to register at hotels.

Migration cards are available at all ports of entry from Russian immigration officials (Border Guards). Every time one enters Russia, he or she needs a new card. Please remember that you can not stay longer on the territory of the Russian Federation than it is stated in the migration card, so be careful filling your migration card out.

To register your Russian visa, you need to present your migration card. Visitors who have not put a registration mark in the migration card will be considered illegal. The only type of visa that is not supposed to be registered is transit visa. Also note that if you are going to stay in Russia for less than 3 days there is no need to register your visa.

If you are staying at a hotel, it will register your visa for you. All you need to do is presenting your Russian visa, passport, and migration card to the hotel administrator. A small registration fee can be imposed, and it usually takes a few minutes to have your visa registered. Those visitors who stay with their friends or relatives or rent an apartment should register their visa through a company that issued an invitation or through a local Passport and Visa Service (UVIR).

Proof of visa registration is a rectangular stamp in the migration card indicating period of validity, date of registration, registration number, name of registering authority and signature of executing officer.

A failure to register Russian visa is likely to result in problems leaving Russia and when trying to reenter Russia in the future. Due to the possibility of random document checks by Russian police, the foreigners should carry their original passports, registered migration cards and visas with them at all times. Failure to provide proper documentation can result in detention or heavy fines. Lost or stolen migration cards cannot be replaced. In this unfortunate case, one should report the loss to regional bodies of domestic affairs domiciliary within 3 days.

Foreign visitors not submitting migration cards during their last stay in the Russian Federation will be restricted to reentering the country.

(sorry for the delay, I'm still traveling and I don't have much access to the Internet)

I didn't ask the hostel, but as they never saw my visa or my migration card, I guess that means they didn't register my visa.
But in any case, there was no problem at all when leaving Russia (by train to Finland), despite a very lengthy check by the Russian immigration officers (the check was very lengthy for everyone, not just for me). They didn't mention registration at all.

Hopefully it won't prevent me to go back to Russia another time, but I haven't tried yet.